9 The fill amounts of a sample of 26 cans of apple juice sho

9). The fill amounts of a sample of 26 cans of apple juice show astandard deviationof 0.06 ounces. You test whether thepopulationvarianceis greater than 0.003. The p-value for this test is:

10). You want to determine whether the variance of sales at two music stores (A and B) are equal. A sample of 26 days of sales at store A provides a sample variance of 800 while a sample of 21 days of sales from store B provides a sample variance of 420.

11). Last year, the variance of the ages of the students at a small liberal arts college was 3.3 years. A recent sample of 81 students from the college provides a variance of 4.1 years. You test to see if there has been a change in the variance of the ages of the students at the college.You obtain a p-vaue of .067. At level of significance of .05, the null hypotheis should be

a.should be rejected

b. none of these answers are correct

c. should be revised

d. should not be rejected

Solution

9.

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   <=   0.054772256  
Ha:    sigma   >   0.054772256  
              
As we can see, this is a    right   tailed test.            
              
Getting the test statistic, as              
s = sample standard deviation =    0.06          
sigmao = hypothesized standard deviation =    0.054772256          

n = sample size =    26          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    30          
Using technology to get the right tailed area of chi^2 = 30,

P(chi^2 > 30) = 0.224289005 [ANSWER]

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